Specific heat, magnetic torque, and magnetization studies of LiCoPO4 olivine are presented. They show that a unique set of physical properties of LiCoPO4 leads to the appearance of features characteristic of two-dimensional Ising systems near the Ne´el temperature TN = 21.6 K and to the appearance of an uncommon effect of the influence of a magnetic field on the magnetocrystalline anisotropy. The latter effect manifests itself as a first-order transition, discovered at ∼9 K, induced by a magnetic field of 8 T. The physical nature of this transition was explained, and a model describing experimental dependences satisfactorily was proposed.